First, since the Gini index is non-differentiable, [1]} proposed a differentiable surrogate using the standard deviation (std) instead, which we refer to as eq. exposure:
\(F^{\rm eq}(P) = \sum _{i=1}^n u_i(P) - \frac{\lambda }{m}\sqrt{\sum _{j=1}^m\left(v_j(P) - \frac{1}{m} \sum _{j^{\prime }=1}^m v_{j^{\prime }}(P)\right)^2}\) 
